Best Known (83, 83+25, s)-Nets in Base 32
(83, 83+25, 87385)-Net over F32 — Constructive and digital
Digital (83, 108, 87385)-net over F32, using
- 321 times duplication [i] based on digital (82, 107, 87385)-net over F32, using
- net defined by OOA [i] based on linear OOA(32107, 87385, F32, 25, 25) (dual of [(87385, 25), 2184518, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(32107, 1048621, F32, 25) (dual of [1048621, 1048514, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,7]) [i] based on
- linear OA(3297, 1048577, F32, 25) (dual of [1048577, 1048480, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3257, 1048577, F32, 15) (dual of [1048577, 1048520, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3210, 44, F32, 9) (dual of [44, 34, 10]-code), using
- extended algebraic-geometric code AGe(F,34P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- construction X applied to C([0,12]) ⊂ C([0,7]) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(32107, 1048621, F32, 25) (dual of [1048621, 1048514, 26]-code), using
- net defined by OOA [i] based on linear OOA(32107, 87385, F32, 25, 25) (dual of [(87385, 25), 2184518, 26]-NRT-code), using
(83, 83+25, 174764)-Net in Base 32 — Constructive
(83, 108, 174764)-net in base 32, using
- net defined by OOA [i] based on OOA(32108, 174764, S32, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32108, 2097169, S32, 25), using
- discarding factors based on OA(32108, 2097171, S32, 25), using
- discarding parts of the base [i] based on linear OA(12877, 2097171, F128, 25) (dual of [2097171, 2097094, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(12877, 2097171, F128, 25) (dual of [2097171, 2097094, 26]-code), using
- discarding factors based on OA(32108, 2097171, S32, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32108, 2097169, S32, 25), using
(83, 83+25, 1875766)-Net over F32 — Digital
Digital (83, 108, 1875766)-net over F32, using
(83, 83+25, large)-Net in Base 32 — Upper bound on s
There is no (83, 108, large)-net in base 32, because
- 23 times m-reduction [i] would yield (83, 85, large)-net in base 32, but